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Small improvements to the recipes and examples. (GH-19635)

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* Add underscores to long numbers to improve readability
* Use bigger dataset in the bootstrapping example
* Convert single-server queue example to more useful multi-server queue
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Raymond Hettinger 2020-04-21 16:11:00 -07:00 • committed by GitHub
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Doc/library/random.rst
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@ -425,29 +425,28 @@ Simulations::
>>> def trial(): >>> def trial():
... return choices('HT', cum_weights=(0.60, 1.00), k=7).count('H') >= 5 ... return choices('HT', cum_weights=(0.60, 1.00), k=7).count('H') >= 5
... ...
>>> sum(trial() for i in range(10000)) / 10000 >>> sum(trial() for i in range(10_000)) / 10_000
0.4169 0.4169
>>> # Probability of the median of 5 samples being in middle two quartiles >>> # Probability of the median of 5 samples being in middle two quartiles
>>> def trial(): >>> def trial():
... return 2500 <= sorted(choices(range(10000), k=5))[2] < 7500 ... return 2_500 <= sorted(choices(range(10_000), k=5))[2] < 7_500
... ...
>>> sum(trial() for i in range(10000)) / 10000 >>> sum(trial() for i in range(10_000)) / 10_000
0.7958 0.7958
Example of `statistical bootstrapping Example of `statistical bootstrapping
<https://en.wikipedia.org/wiki/Bootstrapping_(statistics)>`_ using resampling <https://en.wikipedia.org/wiki/Bootstrapping_(statistics)>`_ using resampling
with replacement to estimate a confidence interval for the mean of a sample of with replacement to estimate a confidence interval for the mean of a sample::
size five::
# http://statistics.about.com/od/Applications/a/Example-Of-Bootstrapping.htm # http://statistics.about.com/od/Applications/a/Example-Of-Bootstrapping.htm
from statistics import fmean as mean from statistics import fmean as mean
from random import choices from random import choices
data = 1, 2, 4, 4, 10 data = [41, 50, 29, 37, 81, 30, 73, 63, 20, 35, 68, 22, 60, 31, 95]
means = sorted(mean(choices(data, k=5)) for i in range(20)) means = sorted(mean(choices(data, k=len(data))) for i in range(100))
print(f'The sample mean of {mean(data):.1f} has a 90% confidence ' print(f'The sample mean of {mean(data):.1f} has a 90% confidence '
f'interval from {means[1]:.1f} to {means[-2]:.1f}') f'interval from {means[5]:.1f} to {means[94]:.1f}')
Example of a `resampling permutation test Example of a `resampling permutation test
<https://en.wikipedia.org/wiki/Resampling_(statistics)#Permutation_tests>`_ <https://en.wikipedia.org/wiki/Resampling_(statistics)#Permutation_tests>`_
@ -463,7 +462,7 @@ between the effects of a drug versus a placebo::
placebo = [54, 51, 58, 44, 55, 52, 42, 47, 58, 46] placebo = [54, 51, 58, 44, 55, 52, 42, 47, 58, 46]
observed_diff = mean(drug) - mean(placebo) observed_diff = mean(drug) - mean(placebo)
n = 10000 n = 10_000
count = 0 count = 0
combined = drug + placebo combined = drug + placebo
for i in range(n): for i in range(n):
@ -476,32 +475,29 @@ between the effects of a drug versus a placebo::
print(f'The one-sided p-value of {count / n:.4f} leads us to reject the null') print(f'The one-sided p-value of {count / n:.4f} leads us to reject the null')
print(f'hypothesis that there is no difference between the drug and the placebo.') print(f'hypothesis that there is no difference between the drug and the placebo.')
Simulation of arrival times and service deliveries in a single server queue:: Simulation of arrival times and service deliveries for a multiserver queue::
from heapq import heappush, heappop
from random import expovariate, gauss from random import expovariate, gauss
from statistics import mean, median, stdev from statistics import mean, median, stdev
average_arrival_interval = 5.6 average_arrival_interval = 5.6
average_service_time = 5.0 average_service_time = 15.0
stdev_service_time = 0.5 stdev_service_time = 3.5
num_servers = 3
num_waiting = 0 waits = []
arrivals = [] arrival_time = 0.0
starts = [] servers = [0.0] * num_servers # time when each server becomes available
arrival = service_end = 0.0 for i in range(100_000):
for i in range(20000): arrival_time += expovariate(1.0 / average_arrival_interval)
if arrival <= service_end: next_server_available = heappop(servers)
num_waiting += 1 wait = max(0.0, next_server_available - arrival_time)
arrival += expovariate(1.0 / average_arrival_interval) waits.append(wait)
arrivals.append(arrival) service_duration = gauss(average_service_time, stdev_service_time)
else: service_completed = arrival_time + wait + service_duration
num_waiting -= 1 heappush(servers, service_completed)
service_start = service_end if num_waiting else arrival
service_time = gauss(average_service_time, stdev_service_time)
service_end = service_start + service_time
starts.append(service_start)
waits = [start - arrival for arrival, start in zip(arrivals, starts)]
print(f'Mean wait: {mean(waits):.1f}. Stdev wait: {stdev(waits):.1f}.') print(f'Mean wait: {mean(waits):.1f}. Stdev wait: {stdev(waits):.1f}.')
print(f'Median wait: {median(waits):.1f}. Max wait: {max(waits):.1f}.') print(f'Median wait: {median(waits):.1f}. Max wait: {max(waits):.1f}.')